We use 73 h of stereoscopic data taken with the MAGIC telescopes to investigate the very high-energy (VHE) gamma-ray emission of the Crab pulsar. Our data show a highly significant pulsed signal in the energy range from 50 to 400 GeV in both the main pulse (P1) and the interpulse (P2) phase regions. We provide the widest spectra to date of the VHE components of both peaks, and these spectra extend to the energy range of satellite-borne observatories. The good resolution and background rejection of the stereoscopic MAGIC system allows us to cross-check the correctness of each spectral point of the pulsar by comparison with the corresponding (strong and well-known) Crab nebula flux. The spectra of both P1 and P2 are compatible with power laws with photon indices of 4.0 pm 0.8 (P1) and 3.42 pm 0.26 (P2), respectively, and the ratio P1/P2 between the photon counts of the two pulses is 0.54 pm 0.12. The VHE emission can be understood as an additional component produced by the inverse Compton scattering of secondary and tertiary epm pairs on IR-UV photons.
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